The terminal set is the pair $\webleft (\text{pt},\webleft\{ !_{A}\webright\} _{A\in \text{Obj}\webleft (\mathsf{Sets}\webright )}\webright )$ consisting of:
- The Limit. The punctual set $\text{pt}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ \star \webright\} $.
- The Cone. The collection of maps
\[ \webleft\{ !_{A}\colon A\to \text{pt}\webright\} _{A\in \text{Obj}\webleft (\mathsf{Sets}\webright )} \]
defined by
\[ !_{A}\webleft (a\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\star \]for each $a\in A$ and each $A\in \text{Obj}\webleft (\mathsf{Sets}\webright )$.